Bitcoin network analyzed by network science

Bitcoin
Bitcoin is the most successful virtual currency that was developed by Satoshi Nakamoto in 2008. The base of the system is an open-source software that has two main functions. First of all, it determines the supply of bitcoin by controlling the mechanism of bitcoin creation. Secondly, it should also prevent double-spending of bitcoins, as there is no central authority that would be able to control the money flow. The main idea behind creating bitcoin was to develop a currency which is independent of any authorities (like governments, banks and central banks) and lacks or at least minimizes transaction costs. Anonymity is also a key in the popularity of bitcoin.
Network Science tools to analyze the system
Looking at the system as a graph where the nodes are the users and the edges are the transactions one can analyze this payment system by the tools of network science. It is fruitful to do so as this approach offers special insights regarding the connections between the transactors.
Network description
The network of bitcoin can be described by the nodes and the links which are the active users and the transactions in a given period.

Annika Baumann, Benjamin Fabian and Matthias Lischke analyzed an extensive dataset that was constructed by Ivan Brugere. The dataset contains 6.3 million nodes (representing public keys to send or receive bitcoin) and more than 37.4 million links (representing transactions). The table below contains the summary of the descriptive statistics of the dataset.
Basic statistics
These statistics describe the dataset that was analyzed by Baumann, Fabian and Lischke.
* Total number of nodes: 6336769
* Number of links (transactions): 37450461
* Degree distribution: The degree distribution seems to converge to a distribution that corresponds to scale-free networks. This result shows that there are a few hubs who have large degrees while the majority of the users have low degrees. It is likely that the exchanges, bitcoin miners and also laundries are among the hubs. According to Baumann, Fabian and Lischke, it is possible to identify some of these big participants through blockchain.info.
* Average clustering coefficient: The high number of average clustering coefficient suggests a small world network. If the bitcoin network was a random network this metric would be close to zero.
* Average degree: In the sample of 03.01.2009 - 10.04.2013 the average degree is 0,169.
Average path length is calculated only on the transactions that are over 50.000 bitcoin. The result is 11 disjoint subgraphs. The average path lengths are calculated on these subgraphs.
* Largest average path length of the largest connected subgraph: 125,083. This high length indicates ineffinciency in the transaction network, or it is also possible that it is a result of the intention of hiding the transaction
* Shortest average path length of the shortest connected subgraph: 1,0
Special facts of the bitcoin network
Accorindg to Ron and Shamir most of the bitcoins are not in circulation. They also analyzed the size of the amounts that are most often sent and found that most transactions involve only low amount of bitcoins. They observed that more than the one third of the transactions were lower than 1 bitcoin and more than the half of the transactions were lower than 10 bitcoin.
These authors also tried to unhide the anonymity of several big participants. They described special patterns that can help in deanonymizing transactions:
*Fork-merge pattern: high amount of money ($90.000) sent through a long chain of BTC wallets divided into parts and arrived to the same destination.

*Binary tree-like distribution: A certain amount of bitcoins is separated into two parts and sent to two addresses. Then these smaller amounts are splitted again and sent to two-two addresses and this chain is kept going further.
*Saving accounts: most of the bitcoins does not circulate in the system, but they are actually form a mean of savings. This phenomena can be seen by the analysis of an almost 30-step-long chain of bitcoin transaction in which always the same amount of bitcoin is sent forward unless it arrived to the final address. The amount has not been sent after arrival up to the time of the analysis.

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